684,321

3 × 11 × 89 × 233

684,321 has digital root 6. The neighboring primes are 684311 and 684329; its proper-divisor sum differs from the starting integer by -357,762.

Prime Factor Structure

Factorization String 3 × 11 × 89 × 233

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 1,010,880

Proper Divisor Sum 326,559

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #684311 ← → #684329

Radix Representation

Decimal	684321
Binary	10100111000100100001 (20 bits)
Octal	0o2470441
Hexadecimal	0xA7121

Divisor Catalog (16)

1 3 11 33 89 233 267 699 979 2,563 2,937 7,689 20,737 62,211 228,107 684,321

Collatz Trajectory (53 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

684,321 2,052,964 1,026,482 513,241 1,539,724 769,862 384,931 1,154,794 577,397 1,732,192 866,096 433,048 216,524 108,262 54,131 162,394 81,197 243,592 121,796 60,898 30,449 91,348 45,674 22,837 68,512 34,256 17,128 8,564 4,282 2,141 6,424 3,212 1,606 803 2,410 1,205 3,616 1,808 904 452 226 113 340 170 85 256 128 64 32 16 8 4 2 1

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